2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60082We consider the sigma models where the base metric is proportional to the metric of the configuration space. We show that the corresponding sigma model equation admits a Lax pair. We also show that this type of sigma models in two dimensions are intimately related to the minimal surfaces in a flat pseudo Riemannian 3-space. We define two dimensional surfaces conformally related to the minimal surfaces in flat three dimensional geometries which enable us to give a construction of the metrics of some even dimensional Ricci flat pseudo Riemannian geometries.Latex file (amssymb), 12 pages. A talk presented (based on the work in Math.DG/0006041) in ``Geometry, Integrability, and Quantization'' July 7-15, 2000 Varna-BulgariaDifferential Geometrytext